Let x ∈ R. Prove that if x<0, then 2x2 − 4x + 4 > 0.

Q: Prove that for all a € R, 0 < r² + 2 VI

A: Prove the following

Q: Let x, y e Z. Prove that if 3x+7y is odd or 5x + 6y is even, then x or y is even.

A: We have given that for x,y belongs to integers. If 3x+7y is odd or 5x+6y is even then x or y is even…

Q: Let x, y, z E R. Prove that if x – 2y + 3z is odd, then 4xy – 6z is even.

A:

Q: Prove that if h E L'(R) and [ h= 0 for all s E R, then h = 0.

A: Use the Leibniz integral rule: For ∫axbx fx, tdt Where -∞&lt;ax, bx&lt;∞ We have, ddx∫axbx fx,…

Q: Let x, y E R. Prove that if 21x + 35y = 45, then x and y are not both integers.

A:

Q: Prove that K = {x+yv3 ] x, y E Z} is a subring of R.

A:

Q: Let r = xi + yj + zk and let r = ||r||. Prove that

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Prove that the following relationship is true: nCr + nCr + 1 = n + 1Cr + 1

A:

Q: Show that For all z E C, with z # 0, then: |z/²z=1 = z

A:

Q: Let C = {r : r E Z}. (a) Show that CnQ0. (le. show C contains a rational.)

A:

Q: Show that f(x) = x4 + 4.x + c has at most two real roots for any umber c.

A: Consider the given equation. fx=x4+4x+c Case 1: When c&gt;0. No sign change, by Descartes rule of…

Q: For any x ER, prove that there exists q E Z such that q-1<r <q.

A:

Q: let r ∈ R\ Q. prove that for all a,b,c ∈ Q, a+br=cr iff a=0 and b=c.

A:

Q: OVESTON Prove that A is inveitine if at0 and at b l Gind The pivos 9 A %3D a a

A:

Q: Let f(2)=³ and let C = {z € C : |z| = 1}, described in the positive sense. Determine the value of Ac…

A: Given that             fz=z4-5z2      and    C=z∈ℂ : z=1.

Q: J prove that for 0 <r<R

A:

Q: prove that erf (x) dx =o

A: To prove: ∫−aaerfxdx=0

Q: Prove that d (sec"x)= 1.

A:

Q: Show that if x ~ Nm (u, 2), where N is positive definite, then (x – u)'N-I (x – µ) ~ Xm: 2

A: Given  x~Nmμ,Ω, where Ω is positive definite.

Q: Let x e R,-1. Prove that VNEN (1+x)" >1+ nx

A:

Q: U prove that In (l+x)) 2.

A:

Q: Let a and b be any real numbers. Prove that Cov (ax, by) = abCov (x, y).

A:

Q: if x, y>o such that x Sy then Vã svy Prove by direct method

A:

Q: Show that f: R → R defined as f(a) = 3a³- 4 is a one to one %3D iuicuon.

A:

Q: Prove that for all values of the constant A, eAInt = e In.

A:

Q: The zero-product principle states that if AB 0, then

A: If AB = 0Then zero-product principle states that this is possible only if - A = 0andB = 0

Q: Let a in F_p, a is non zero then show

A:

Q: If x > 0, prove that T - In (1+ x) > 2+2x

A: Using derivative

Q: In Let x, y ER" be given. (a) If ||x|| = ||y|| = 1 and x - y = 1, show that x = y. (b) If ||x|| ≤ 1…

A:

Q: If e denotes the unity element in an integral domain D, prove that me · ne = (mn)e for all т, п € Z

A:

Q: Q3/A/ Prove that ) + ",) = C). %3D إضافة ملف

A: As per our guideline we are allowed to do 1 question at a time. I think you hav already done 2…

Q: Show that f(x) = x³ + 2x + 20 is irreducible over Q.

A: We say that a polynomial is irreducible if it cannot be expressed as a product of two non-constant…

Q: Show that for any positive integers i and j with i > j, we have T;(x)T;(x) = [Ti+;(x) +T;-j(x)].

A: we have to show, for any positive integers i and j with i&gt;j TixTjx=12Ti+jx+Ti-jx Now, we know…

Q: Show that f(x)= x14 – 6x + 75 is irreducible over Q.

A: Eisenstein's Irreducibility Criterion: Let us consider polynomial…

Q: find the root of the fnmetion ーX FCx)= ē^ _ x which lies betwen (o %3D

A:

Q: Prove that if X₁X and Ync, then (Xn, Yn) (X, c).

A: For a sequence of random variables X1, X2, X3,... to converge to a random variable X, we must have…

Q: Find the source Q cx) Such that the So lutiim Uckit) of + Q(x) 2 ə x² 0 < x <∞ | U(x,o) = 0

A: given equation ∂u∂t=k∂2u∂x2+Qx ,       -∞&lt;x&lt;∞            ...iux,0=0 claim- find the source Qx…

Q: Let r E Rt. Prove that if z – 2x2 +2 2021. -

A: Let x2=t, Now if x∈R+⇒t∈R+ ⇒t2-2t+2≤0⇒t-12+1≤0⇒t-12≤-1which is not possible for any value of t, for…

Q: let X~~ Per(P) Prove ô is unbiare if ô-X let x exp(0) Prave e is unbiar

A: Introduction: One random variable follows Bernoulli with parameter p and other random variable…

Q: Prove that for every y E R, there exists a unique x E R such that 2(x – 1)3 – y = 0. %3D

A:

Q: For Z= x²csc y,prove that Zxy is equal to Zyx

A: Given that,    z=x2csc y

Q: 2. Use a theorem to find the ff. Zx if yz? + z = 5xy – 1.

A: Find out the zx when function is given as yz2+z=5xy-1 or yz2+z-5xy+1=0

Q: Let x, y,p E Z, where p is prime. Prove that x2 – p²y – p + 0. (Hint: you may use without proof that…

A: Solution :-

Q: Prove that S[x] = {a+bx where a,b in R} is subring ℝ[x].

A:

Q: Find conditions on a, b, c, and d such that

A: Find conditions on a, b, c, and d such that  B=abcd commutes with both 1000 and 0001 For any matrix…

Q: I. Solve using De Moivre's Theorem. Given that z is not real number and z = 1, show that w = z-1 z+1

A:

Q: Let x, y e Z. Prove that if 3x + 7y is odd or 5x + 6y is even, then x or y is even.

A:

Q: Prove that if X ⊆ Y then X ∩ Z ⊆ Y ∩ Z.

A: To prove this we will take an element from X∩Z and show that 'a' also belongs to Y∩Z.